Question

Hello, I’m struggling. I need help (: with number 5

Answer 1

Consider the following triangle (not in scale):

We know that:

`\begin{gathered} tan(A)=(3)/(4)tan(B)=(x)/(y) \\ tan(A)=(sin(A))/(cos(A)) \\ tan(B)=(sin(B))/(cos(B)) \\ (s\imaginaryI n(A))/(cos(A))=(3)/(4)\cdot(s\imaginaryI n(B))/(cos(B)) \\ sin(A)=(3)/(4)\cdot(sina(B)\cdot cos(A))/(cos(B))=(3)/(4)\cdot((y)/(h)\cdot(y)/(h))/((x)/(h))=(3)/(4)\cdot(y^2)/(h\cdot x) \end{gathered}`

Applying the same steps for sin(B), cos (A) and cos(B), we have:

`\begin{gathered} sin(B)=(4)/(3)\cdot(x^2)/(h\cdot y) \\ cos(A)=sin(B)=(4)/(3)\cdot(x^2)/(h\cdot y) \\ cos(B)=sin(A)=(3)/(4)\cdot(y^2)/(h\cdot x) \end{gathered}`